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The Placidus house system at high latitudes
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Ruud66



Joined: 05 Apr 2009
Posts: 46
Location: Amsterdam, Netherlands

Posted: Sun Jul 29, 2018 9:18 am    Post subject: Reply with quote

waybread wrote:
Ruud, is there another possibility? That houses are not so important universally?

I'm always struck by how house cusps change depending upon the system used. For example, I have a late degree of Virgo rising, and my chart looks really different depending upon whether I use a quadrant system, whole signs, or equal houses.

The lack of agreement among house systems historically was a real source of criticism among astrology skeptics.

Waybread,
I wholeheartedly agree with the astrology skeptics in this matter. We astrologers are collectively making fools of ourselves because of the amateuristic way we approach the houses of the horoscope. There are no fundamental theories in astrology of what houses are in their essence, at least, not that I'm aware of. There are many theories why one particular house system is the one and only true, original, best house system, but nothing that integrates the whole arena of domification.

It is true that, in the arctic, almost all house systems are stretched to their limits (and sometimes beyond), but to say that houses are not so important universally..... I'm not sure.
If the houses in a person's horoscope are deemed less important than in other people's horoscopes, aren't you saying then that this person has less of a personal life and is more living collective human life themes in an unfocused way? Isn't that a bit discriminating against that person?
I know that life can be very harsh and limiting in the high north, but surely people can live a relatively normal life in a city like Murmansk?

I do agree with you that some house systems sometimes show a very limited house division (especially the quadrant systems) in the arctic and that this symbolises the limitations of the diurnal motion of the Sun during periods of time in summer and winter.
Wackford, in his article, also tried to descibe this and incorporate it in his understanding of domification in the arctic: http://www.skyscript.co.uk/polar4.html especially in the section under "Seasonal variations and the diurnal cycle: A year within a day."

waybread wrote:
In addition to discrepancies among house systems, planets-in-signs vary widely depending upon whether one uses sidereal vs. tropical zodiacs.

The difference between the tropical zodiac and the sidereal zodiacs is actually quite a valid metaphor. Planetary positions in the tropical zodiac are approached differently than planetary positions in the sidereal zodiacs. A different viewpoint is applied and the kind of astrological questions asked are different. This is one of the reasons that both systems can live happily side by side: you can't mix them. They are really a different approach.

Same is true for the different house systems in my opinion. The meaning of planets in equal houses, for example, have a different application than the meaning of planets in quadrant houses. They are approached with a different question in mind.
Therefore, it is quite possible to have the Sun in the 8th equal house and in the 12th house Placidus, in the same horoscope at an arctic latitude. These two positions mean different things, they are symbolic for a different approach and a different question that needs answering.
How and what exactly: that is something that needs a lot of research.

The problem with the theory of houses at this moment is that everyone seems to think that all the house systems point towards the same thing, the same experience, the same astrological questions.

waybread wrote:
Anyway, I applaud your research and hope you determine what house system works best at high latitudes, if any do.

My position at this moment is therefore, that it is necessary to look at more than one house system in order to get a rounded assessment of a horoscope. One of the equal systems in conjunction with one of the quadrant systems. My personal choice is Equal with Placidus houses.

And I admire your tenacity in trying to understand these matters and keep questioning. This forces me everytime to reassess and reformulate everything. I think that is a valuable growth process.
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waybread



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Posted: Sun Jul 29, 2018 7:13 pm    Post subject: Reply with quote

Ruud66 wrote:
...
Waybread,
I wholeheartedly agree with the astrology skeptics in this matter. We astrologers are collectively making fools of ourselves because of the amateuristic way we approach the houses of the horoscope. There are no fundamental theories in astrology of what houses are in their essence, at least, not that I'm aware of. There are many theories why one particular house system is the one and only true, original, best house system, but nothing that integrates the whole arena of domification.


A really good point, Ruud. During the perennial, "Which house system is best?" debates, I've appreciated Michael Munkasey's guideline that we use the house system that best describes the area of a person's life or event under consideration.

Unfortunately, people oftentimes get into astrology because they don't feel that they understand themselves very well. Sometimes self-knowledge comes from maturity and life experience that a young person does not yet have. Also, adjacent houses sometimes have comparable meanings. For example, the 3rd and 4th can both relate to family matters. Also, a shift of planets from one house to the next might, for example, move the sun into a new house, but then perhaps another important planet moves into the house that the sun vacates. So that house still is an area of focus in the person's life.

But none of this is grounded in theory, or in the mathematics of what a particular system says about the cosmos. (Is there a celestial equator out there, really?? Or is it just a convention?)

Quote:
...If the houses in a person's horoscope are deemed less important than in other people's horoscopes, aren't you saying then that this person has less of a personal life and is more living collective human life themes in an unfocused way? Isn't that a bit discriminating against that person?
I know that life can be very harsh and limiting in the high north, but surely people can live a relatively normal life in a city like Murmansk?


Well, what is "normal" is geographically and culturally relative. However, I note that Ptolemy scarcely used houses, perhaps because in his day they were still known to be based in Egyptian religion. One could use his methods today, involving planetary relationships. I don't think that saying, "Hey, I'm having trouble reading houses for your Murmanks nativity" implies disrespect.

Quote:
The difference between the tropical zodiac and the sidereal zodiacs is actually quite a valid metaphor. Planetary positions in the tropical zodiac are approached differently than planetary positions in the sidereal zodiacs. A different viewpoint is applied and the kind of astrological questions asked are different. This is one of the reasons that both systems can live happily side by side: you can't mix them. They are really a different approach.

Same is true for the different house systems in my opinion. The meaning of planets in equal houses, for example, have a different application than the meaning of planets in quadrant houses. They are approached with a different question in mind.


I think so. But one issue I have for a high latitude chart in, say January, is that traditional astrology deals with day and night births. Correct me if I'm mistaken, but traditionally a day birth has the sun somewhere in houses 7 through 12, i. e., above the AC/DC horizon; whereas a night birth has the sun somewhere in houses 1 through 6, i. e., below the AC/DC horizon. This, to me, makes a horoscope a less accurate stylized picture of what is actually taking place in our geocentric, topocentric experience. While degrees rise and set even when the sun never appears above the horizon, we kind of lose the natural meanings of the day vs. night birth.

Quote:
Therefore, it is quite possible to have the Sun in the 8th equal house and in the 12th house Placidus, in the same horoscope at an arctic latitude. These two positions mean different things, they are symbolic for a different approach and a different question that needs answering.
How and what exactly: that is something that needs a lot of research.


Agreed! I hope you undertake it.

Quote:
The problem with the theory of houses at this moment is that everyone seems to think that all the house systems point towards the same thing, the same experience, the same astrological questions.


Agreed. Obviously different house systems can point to very different experiences, for example, depending upon whether the sun is shown in the 5th or 6th house. But as a foundational principle, yes. If two people are both born at noon, then presumable the sun conjunct MC should confer a similar sense of identity.

Quote:
And I admire your tenacity in trying to understand these matters and keep questioning. This forces me everytime to reassess and reformulate everything. I think that is a valuable growth process.


Thanks very much, Ruud. You are a scholar and a gentleman.
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Ruud66



Joined: 05 Apr 2009
Posts: 46
Location: Amsterdam, Netherlands

Posted: Sat Sep 01, 2018 11:01 am    Post subject: Reply with quote

Paul wrote:
I made an attempt to reply to you and lost it when my internet connection died, so here I go, I'm trying to summarise the points I made in my lost reply. Then I'll hopefully get to go back over some of your points in more detail.

Finally, I have come around to formulating a reply to your post. It is really unfortunate that you lost the more detailed version of it: now I'm not sure if I understand you correctly, as you will see in my replies to each of your statements. I apologise in advance that I seem to punish you at every paragraph.

Paul wrote:
Of course I'm completely in agreement with you regarding the problem really not being one of the modelling of the mundane sphere per se but more to do with how the ecliptic interacts with that. However, I do think it's necessary to perhaps separate the house system's arcs with the actual house system itself - because only when those arcs interact with the ecliptic, for good or bad, do we have an astrological house system.

Quite on the contrary, I'd say! The 'actual' house system is in the mundane arcs. If there are no intermediate cusps and only the four angles, for example, then we still have a full house system on the mundane arcs. And also the positions of planets and points in the houses are not dependend on their relative position to the ecliptic cusps, but they are defined on the mundane arcs.

Paul wrote:
You present a solution which, if I follow it right, is the same or similar to what Michael Wackford presents of Otto A. Ludwig's solution to the problem which isn't, as you rightly highlight, necessarily to do with dividing up the mundane sphere, but rather dealing with the ecliptic's obliquity at the poles. However, to play devil's advocate, if what we're doing with the houses is astrological, and if that astrology focuses upon where the arcs hit the ecliptic, then any 'weirdness' at the ecliptic has to be considered as part of the house system itself.

Again quite on the contrary: the problem of the circumpolar sky is precisely in the dividing up of the mundane sphere! Or more correctly the fundamental definition of the system and how it is seen to divide the sky, or not. The weirdness at the ecliptic is in the eyes of the astrologer: if a certain solution (e.g. the Placidus system of houses) gives results at lower latitudes that the majority of astrologers are very happy about, then why should the exact same, identical solution at higher latitudes suddenly be so problematic? The only thing that happened is that the 12-fold division, that astrologers are addicted to, isn't happening anymore. But the 12-fold division is still present in the mundane arcs. It is a misconception that the ecliptic application of the system is what it is all about.

Paul wrote:
In other words, all the equal, whole and porphyry house system users must surely, they think, avoid this problem because the only circle they care about is the ecliptic and if Placidus has problems with the ecliptic then Placidus has problems full stop. In the other thread, which I'll link to here so people can follow it later on, what I try to do is expose that myth. This isn't a problem of Placidus, this is a problem which *all* the house systems, including equal, porphyry and whole have to deal with, and they all make assumptions in how to do that.

http://skyscript.co.uk/forums/viewtopic.php?t=9618

And here we are in complete agreement. Which gives me the impression that I don't understand you correctly in what you have written further above.

Paul wrote:
Another focus you have is the 'problem' of placidus houses as being chiefly a problem of calculation - the problem is that the 'normal' way of calculating the houses breaks the house system model we expect and so something has to be done.

Actually, what I see as the main problem is the lack of a definition of what the system really is conceptually. Calculation is irrelevant if you don't really know what a system is conceptually.

Paul wrote:
Of course when it comes time to do that "something" we have to make assumptions about the MC, but, in following your posts, we also have to imagine that Placidus arcs are the most important part of the house system - but I think it's arguable to also imagine that actually the only important part where it comes to astrological use is where the cusps interact with the ecliptic. The houses, as we use them, are not defined along the space defined by the house arcs - in other words if a house arc comes slanting in at some angle to the house cusp, say at 60% or something, we completely ignore that, and then imagine the houses as being perpendicular to that point, as though it were drawing a new arc from that point to the pole of the ecliptic.

This is exactly the misconception I talked about above.

Paul wrote:
Of course you know all this, I'm just highlighting the point that the Placidus arcs are all but forgotten or ignore the moment we intersect with the ecliptic - at least in regards how we currently tend to use the houses. It may be a whole other debate as to whether or not we should be doing that in the first place.

Indeed. Maybe it could be useful, especially with arctic charts, to make a second horoscope drawing with just the house placements in a twelve-fold pie-shaped chart, using the mundo positions that Ed Falis is a great proponent of.

Paul wrote:
With that in mind though I think the focus shouldn't be on the house arcs and their calculation, but rather in what we're expecting from the houses and we think they're modelling or attempting to model - even if that model becomes abstracted or imagined as an idealised model. With that in mind, I think we ought to really be focusing on what we think the houses are doing and then finding a computational solution.

If you mean by this that you want to look for a fundamental definition and start from there, then I'm in agreement completely.

Paul wrote:
I think this is important, because if part of your definition, and indeed symbolic landscape, astrologically speaking, is to imagine the MC as being the culminating point of a planet, then that would lead to one way of calculating the MC and the houses which could be quite different from if you imagine the MC as chiefly the culminating point above the horizon, or if it's the most southerly (or northerly in the southern hemisphere) point etc.

The kind of definition you have for the MC is important, yes, but it should follow logically from the core definition of the house system you're using. In the case of Placidus houses, this can only be the culminating point of the ecliptic. Whether this is below or above the horizon is not relevant to the system. See also my last remarks.

Paul wrote:
Why you might care would be if your astrological interpretations tie into that kind of symbolism.

What this means, for me, at least, is that for the quadrant houses, you may have multiple variants of the house, so there isn't *a* Placidus House System, but rather Placidus House Systems plural.

This of course is quite an abhorrent thing to imagine and quite against perhaps our natural instincts - it would make things complex and difficult to use, but perhaps it is the most truthful to an astrologer's toolkit.

The other definitions of the MC can be true in other house systems. Each house system can only have one definition, however. Otherwise you contradict yourself.

Paul wrote:
However, as I argue on the other thread, to some degree what I really believe is that none of this actually matters in the sense that actually a fixation or focus on calculation masks a much bigger problem to do with astrological interpretation. If we imagine the MC carries connotations of visibility and acclaim and recognition, then how does that gel with any house system that allows the 'MC' to be the most hidden part of the sky and completely unrecognisable etc.

That's the real problem for me, and everything else is something of a distraction and it's a problem that nobody really seems to want to focus on very often, but I'll save all those arguments for the other thread.

I'm hoping to get time to reply more fully to your posts in more detail soon, but wanted to make a start.

My present understanding of the MC is that it is one of the projections of the Zenith. The key measurement/geometry point is the Zenith: it is the location itself as it is projected onto the celestial sphere, it is the topocentre.
If you project the Zenith over the Meridian (a mundane circle) then you always arrive at the MC, even if it is below the horizon. If you project the Zenith onto the ecliptic in the ecliptic system itself, you will always arrive at the Nonagesimal, providing that the Nonagesimal is defined as the point 90 degrees away from the Ascendant that is above the horizon. This is because only that point is the projection of the Zenith onto the ecliptic.

The Nonagesimal should be the 10th cusp in the Equal system. If the Nonagesimal is defined as always being above the horizon and the Ascendant is retrograde, it should mean that the Equal system must be inverted: the 12th house is then below the Ascendant in the chart drawing and the 1st house above it, the 10th house is then where you would expect the 3rd house to be in a normal chart. This is one of the hypotheses I would like to see investigated and see how that fits a person's life.

The MC's definition in the systems that use the house circles that run through the north- and south points of the horizon, is the intersection of the ecliptic and the meridian that is above the horizon. This is because that is the projection of the Zenith onto the ecliptic, using those house circles. I'm talking about the systems of Campanus, Regiomontanus, Abenragel, and others. I have a personal bias against these systems, I'm afraid.

The MC's definition in Placidus houses is the culminating point of the ecliptic, even if that point is below the horizon, because that is the mundane projection of the Zenith onto the ecliptic. My present understanding is that an "MC" that is circumpolar below the horizon is a different kind of point than an MC that is above the horizon. For one thing, the circumpolar MC below the horizon is not a cusp of the 10th house, but of the circumpolar 1st, at least in the Placidus system. Therefore this point does carry the meaning of a pivot, a point that is most angular, but not the notion of being most visible.
Similarly, the IC that is circumpolar above the horizon is not a cusp of the 4th, but of the circumpolar 7th. These circumpolar 1st and 7th houses arise directly from the core definition of the Placidus system, as I tried to explain in my first posts on this thread, but they do not carry the idea of rising and setting, as the non-circumpolar 1st and 7th houses do.

I hope you still want to talk to me after all this. Very Happy As always, I enjoy sharing and comparing ideas with you on this subject, even if it resembles a wrestling match at times.
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Paul
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Posted: Wed Sep 05, 2018 12:20 pm    Post subject: Reply with quote

Ruud66 wrote:

I'm not sure if I understand you correctly, as you will see in my replies to each of your statements. I apologise in advance that I seem to punish you at every paragraph. 


I think we may be simply missing each other’s points at times - I don’t think any of the points you make here ‘punish’ me or any of the points I’ve made, which makes me think we have a different context in mind.

Ruud66 wrote:

Paul wrote:

because only when those arcs interact with the ecliptic, for good or bad, do we have an astrological house system

Quite on the contrary, I'd say! The 'actual' house system is in the mundane arcs.


I explain this further in my post which you later refer to. I’m not sure if this is the ‘punishing’ you refer to - as far as I can see, it’s the major piece of disagreement in your post? I suspect it is, and that we have a disagreement here which causes the rest of my post to be more easily misunderstood. Bare with me whilst I elaborate more. I did this in my more lengthy reply I had lost so I may have skipped through this in my post.

To re-explain what I said further in the post of mind you quoted this from, imagine the mundane arc intersects the ecliptic at, say 70º - the point at which a mundane arc becomes a house system, as it’s currently used by astrologers, is that this point is subsequently projected at 90º arc. In other words you can have a planet/point which is nestled within the, for example, 11th house and 12th house arcs and we may well imagine that this point/planet is imagined as “in” the 11th house. But by the time those arcs intersect with the ecliptic and are subsequently projected at 90º from the ecliptic, we might find that actually that planet or point is in the 12th house instead.

Now, don’t get me wrong. You may not like this, you may not agree with this, this may not be how you formulate house divisions yourself, but it remains the case, whether anybody likes it or not, that this is precisely what astrological software does (I’m sure there are exceptions but I’m talking by far the majority) - whether we imagine it as a planet with latitude off the line of the ecliptic, or whether we imagine it as some star/point far off the ecliptic itself, the reality is that house systems, as per astrological software, finds the intersection of a given arc with the ecliptic and projects perpindicularly from that point.

To really make this explicit consider the following image (my apologies for the quality, I really rushed through creating this):

https://i.imgur.com/YS6XhXM.gif


I’ve labelled what we can imagine is the second house arc and the third house arc, the intersect the ecliptic at an angle and I’ve demarcated in dotted lines, and shaded in blue, what astrological software typically would determine to be the second house. As we can see, Venus falls between the second and third house arcs, and yet is not found in the second house itself. To repeat my point then, only when these arcs interact with the ecliptic, for good or bad, do we have an astrological house system - I take it you adopt the ‘bad’ part of the “for good or bad”.

Now you may wish to adopt a mundane house system where the entire mundane arc demarcates the area between houses, but this is typically not what astrological software, or indeed tables or formulae for house division that are done by hand.

To return to my point then, my first challenge or point of disagreement, is that we ought to separate the mundane house arcs from the astrological houses themselves - at least insofar as actual astrologers use them in practice.

Quote:
Again quite on the contrary: the problem of the circumpolar sky is precisely in the dividing up of the mundane sphere!


As I try to highlight, it is not JUST dividing up the circumpolar sky via the mundane arcs, it is dividing up the circumpolar sky by mundane arc INCLUDING where those arcs intersect with the ecliptic and projecting perpendicularly from those points - because that is precisely what software does outside the circumpolar sky. It is therefore not enough to focus exclusively on the mundane arcs. Astrologers, typically, do not occupy the spaces between those arcs as the ‘houses’. Now whether or not they should is entirely another matter. So in other words the fact that these arcs intersect/hit the ecliptic needs to be taken account of, because, in practice, it is the phenomena happening along the ecliptic band that we typically want to enquire or measure when we’re using houses. Remember: I’m not advocating a reinvention of what houses should be or how they’re calculated, you may be, but that is not what I’m doing, so my points are not related to that - my points are to point out, essentially, where the emperor has no clothes, and in doing so hope to draw attention to the fact that all the houses have problems at the poles so we can have a more reasoned discussion of house systems generally, but including “problems” at the poles. As of writing, the typical consensus is that “placidus houses don’t work at extreme latitudes” and often followed by something like “whole/equal/porphyry are perfect and have no problems at extreme latitudes”. An extension of this logic is “I use whole sign houses/equal houses because they work everywhere all over the globe and not just at moderate latitudes”.

So, this brings us to:

Quote:
The only thing that happened is that the 12-fold division, that astrologers are addicted to, isn't happening anymore. But the 12-fold division is still present in the mundane arcs. It is a misconception that the ecliptic application of the system is what it is all about. 


I disagree with you here. I think insomuch as astrologers typically calculate houses by way of their intersection with the ecliptic (which typically astrological software and conventions ‘by hand’ also adopt) then we cannot ignore the elephant in the room - the ecliptic. We may not like this, this may muddy the calcluations, but like it or not, that is how the houses are calculated. If in doing so we run into problems, then we run into problems full stop. We cannot simply imagine that we shouldn’t be obsessed/attached to the ecliptic (incidentally I don’t disagree), because like it or like it not, that is how astrologers in practice employ their houses. They expect to be able to do things like have house rulers - well how do we get house rulers except by examining the place in which the house arc intersects with the line of the ecliptic?
I think this is our major source of dispute here - for me the astrological house system as it is actually used by astrologers cannot be so easily separated from the ecliptic.

Quote:
Actually, what I see as the main problem is the lack of a definition of what the system really is conceptually. Calculation is irrelevant if you don't really know what a system is conceptually. 


This is a good point. I would be interested in hearing how you conceptualise the placidus system, taking care to limit the conceptualisation to a line or two. It would be useful to frame it in terms of experiential qualities. In other words let’s put aside calculation, and put aside HOW you calculate or draw up placidus arcs, let’s imagine we track a planet/point as it rises, culminates, sets etc. and conceptualise it in placidean logic. How might you do this? A naive person may say something like “it’s based on a proportional division of time for that point to rise and culminate above the horizon, and subsequently set, anticulminate below the horizon and subsequently rise”. Obviously it’s far too broad a definition, but we already realise that is a definition that simply doesn’t work at the poles. What would you prefer or think captures it better?

Quote:
If you mean by this that you want to look for a fundamental definition and start from there, then I'm in agreement completely. 


Pretty much, you made some attempt at this, but then I disagreed with how you framed what you expect from a house system, in my view it was too narrow and ended up essentially precluding everything but placidus. For me, I would start off pretty broad and say that a house system is a tool used by astrologers to attempt to frame the position of given point or planet in reference to the zodiac and describe its primary motion at a given moment in time in relation to astronomical points (angles).
Let’s keep it short - over to you.

Quote:
The kind of definition you have for the MC is important, yes, but it should follow logically from the core definition of the house system you're using. In the case of Placidus houses, this can only be the culminating point of the ecliptic. Whether this is below or above the horizon is not relevant to the system. See also my last remarks. 


Actually this is exactly my point - so let me make it more explicit. Astrologers themselves, when using a house system, do not realise the problem of defining the MC may not make sense in the house system they’re using. They may even hold contradictory positions about what the MC is or what they expect it to be. They may think it’s perfectly reasonable to assume the MC is always to the south and always above the horizon, for example. This is important not just in terms of calculating the houses, but, in a kind of orthopraxy, how they actually use the houses. If our horary astrologer is looking for that missing key, and he sees it at the MC, is it reasonable or not for him/her to expect that the key is to the south, or indeed somewhere heightened or visible?

It’s these problems that in many ways I find more to the heart of the problem of house division at extreme latitudes - the problems of calculation, are, for me, secondary to this. This is the real problem, and, for me, any solution we come up with technically or in terms of calculation, should be attempting to solve (if possible) this problem. I suspect it cannot be done. As a result, rather than try to solve it, what I’m trying to do with my posts is highlight the problem itself.

This whole thing kicked off, for me, when I realised that a whole sign house user believed that his house system could be used anywhere on the globe without problem, and my crummy placidus system was a limping mess that collapsed in a heap at the poles. When actually the very same problems, in my opinion, that are “breaking” placidus, are equally breaking whole sign houses - it’s just that whole sign house users don’t actually realise what the hell is going on or why it’s a problem. If the Mc isn’t needed to calcluate the houses, it’s reasonable, they believe, to imagine that they don’t need to define or think about how the MC is conceptualised. They are dead wrong in that assumption.

Quote:
If you project the Zenith over the Meridian (a mundane circle) then you always arrive at the MC, even if it is below the horizon.


Yes, but you will also get the IC. Which one is which? Part of the problem is if you ‘go north’ or ‘go south’ along the meridian and expect to always hit one or the other one first. The reality is that something like a culminating point is a fixed position of something which is conceptualised by tracking the motion of a given thing - that’s what makes it often quite difficult for people to conceptualise. If I just took your definition and I always go south (in the northern hemisphere), then I will reach the MC below the horizon. But if my astrological MC is that it’s a heightened visible point above the horizon around which the planets appear to ‘swing’ or ‘pivot’ (kentron - a centre, a pivot etc. as well as a prodding point in the ancient texts) then, to be blunt, I’m screwed. To keep repeating myself, the problem then isn’t calculation, it’s understanding and practice of astrologers - it’s managing astrologers’ expectations.

I more or less agree or am ambivalent about the rest of your post so going to leave it here. I made sure to write this up in a separate file before posting so I wouldn’t lose it. It took a bit of time to create that pretty crappy image as I’m a bit out of practice so be gentle!

[/quote]I hope you still want to talk to me after all this. Very Happy As always, I enjoy sharing and comparing ideas with you on this subject, even if it resembles a wrestling match at times.
[/quote]

Quote honestly I could talk about this stuff all day provided everyone is on the same page as me - one of trying to highlight, recognise, and maybe even solve certain issues of house division. I don't really have much of a horse in the race because ultimately I just think it's better to let people do whatever they want with their houses. But from time to time I will see some odd statements about houses, much of which stem from ignorance, and I think it's better to try to discuss the elephants in the room, pluck the hydra's head out of the shadows and actually examine what's really going on here. That way we can hopefully move away, in time, from statements like "Only whole sign and equal houses work reliably at the polar regions" etc.
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Ruud66



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Posted: Thu Sep 06, 2018 12:41 pm    Post subject: Reply with quote

Paul wrote:
I think we may be simply missing each other’s points at times - I don’t think any of the points you make here ‘punish’ me or any of the points I’ve made, which makes me think we have a different context in mind.

That is good to hear. Everytime I directly contradict you, it is not because I want to accuse you of something, but I want to highten the contrast in order to make a particular issue clearer.

About your post: I think I'm beginning to understand your approach more and more. A discussion on a forum is actually quite a difficult form of discussing things. Many of these misunderstandings would surface in minutes if you would discuss them life and in person.

Before I go deeply into my reply to the things you say in your post, I want to clear up two issues with you that may or may not color the way you see things.

First about the house systems and the ecliptic:

Paul wrote:
To really make this explicit consider the following image (...):
https://i.imgur.com/YS6XhXM.gif

Paul wrote:
I think this is our major source of dispute here - for me the astrological house system as it is actually used by astrologers cannot be so easily separated from the ecliptic.

I understand your image and your arguments, but you confuse two concepts here: on the one hand the house system and on the other hand the projection of the sky onto the ecliptic.
I know you want to get to the way the vast majority of astrologers use the houses, but bear with me while I make these (to me) fundamental points:

Astrologers and the software they use create the horoscope by projecting all planets and points onto the ecliptic. It is these ecliptic projections that make up the horoscope. This is how we treat all celestial objects and points that we see interacting with the earth, and thus ouselves, through the plane of the secondary motion of the earth. Most astrologers (and most software) take this material and put that into the house system.

On this thread I concentrate on the Placidus house system and what I try to make clear is that a house system like Placidus models the primary motion of the sky (not the secondary motion as you, of course, know) and as such is completely mundane. But we already projected all planets, points, stars and all the rest onto the ecliptic in an earlier stage. So, maybe it seems as if the house system is defined on the ecliptic too, but it is not. The house positions are not due to a perpendicular projection of the house cusps on either side of the ecliptic, but an earlier projection of the planets onto the ecliptic.

It has become my understanding that the house system is not based on the ecliptic, because of what can happen in the horoscope beyond the polar circles, where in the Placidus system, houses can run direct and retrograde through the zodiac and the relative house position can change direction mid-house.

Let's imagine the situation in a horoscope for 70N latitude at a sidereal time of 20:08 hours. You can see a picture of this horoscope in example 6 in the Readme introduction to the Table of Arctic Houses, the Placidus table of houses for 60N-89N latitude that I created. https://www.astro.com/swisseph/Table_Arctic_Placidus_readme.pdf

Then let's imagine the Sun at 2°00' Aquarius: it is conjunct the Ascendant at 0°43' Aquarius, but it is situated in the 10th house, right before the cusp of the 11th at 0°50' Aquarius. The Ascendant, cusp 12 and cusp 11 are all in the first degree of Aquarius and RETROGRADE. In my read-me introduction to the Table of Arctic Houses, I explain that this means two things: 1. the cusps run in retrograde motion throught he zodiac (like a retrograde planet) and 2. the order of the houses is inverted around the cusp(s). This does not mean that the primary motion has been inverted, which is, of course, impossible.

The Sun, on it own semi-arc, has therefore just left the 11th house and entered the very last part of the 10th. Then let us imagine Venus and put it with zero latitude at 7°00' Aquarius. This position is also in the same 10th house, but here the house system is in direct motion. There is another cusp 11 at 7°43' Aquarius, also in direct motion. This means that Venus is at exactly the same phase on its mundane arc as the Sun is: Venus has just entered the very last part of the 10th house on its own semi-arc aswell. If you interpet the house system for this situation as having only meaning on the ecliptic, then it is unintelligible what is happening here. There is no visible reason why the house system behaves in such a crazy way, if you just observe it in the ecliptic.

Of course, Venus can have a latitude of up to eight degrees north or south of the ecliptic and in this horoscope that could mean that the actual position of Venus in the sky can be circumpolar below the horizon (in the circumpolar 1st house), while its ecliptic position is in the 10th house. But it is almost always the ecliptic positions of the planets we use for interpretation of a natal horoscope.

This leaves your argument about the house rulers.
Yes, a house ruler is dependend on the house curve intersecting with the ecliptic, creating a cusp. But as you can see in the majority of the examples in my Readme article: these horoscopes don't have all house curves intersecting with the ecliptic. Here I must agree with the astrologers who say that the Placidus system of houses breaks down in the arctic: but only in the sense that the mundane arcs can fail to interact with the ecliptic at one time and can interact with the ecliptic up to four times at another time.
To me this means that a mundane system like Placidus houses is not the right choice for finding your house rulers, not in the arctic (obviously,) and also not on the rest of the earth! (Sorry, folks ...) I would use Equal houses for that. So only in this last argument can I agree with your view on the ecliptic use of a house system.

The second issue is about the definition of the MC:

Paul wrote:
Yes, but you will also get the IC. Which one is which?

Actually, no, you will not get the IC.
What you refer to is the definition of the MC/IC as the intersection of the meridian circle with the ecliptic. If you use that definition, then the MC and IC are not differentiated and if you modify that definition, you keep running into problems. I have given this whole conundrum a lot of thought and came up with the definition that the different solutions of the MC and also the Nonagesimal are all projections of the Zenith. Each point is a different kind of projection of the Zenith. This is also close to the position of Ed that he contributed in the other thread on arctic charts.

If you project the Zenith onto the ecliptic in the mundane system, then you will always get the MC described as the culmination point of the ecliptic. You will never get the IC described as the anti-culmination point of the ecliptic. In the mundane system you project points using the meridian circles that run from celestial pole to the other celestial pole. And the Zenith is always on one side of the celestial poles, forming unambiguously the projection onto the ecliptic that I described above.
An MC defined in this way could be below the horizon. Yet it retains its symbolism of most visible and prominent because it is derived from the Zenith, of which it is just a projection.

The MC as used in the systems with Campanus-style house circles, will always be above the horizon, because these house circles are defined as running between the north- and south point of the horizon. The Zenith will always be on the semicircle that is above the horizon, forming a projection onto the ecliptic that will always be above the horizon aswell. The fact that the house circle that runs through the Zenith is also a meridian, is convenient, but irrelevant.

Finally, the projection of the Zenith onto the ecliptic in the ecliptic system itself, will be a point 90° away from the Ascendant that happens to be above the horizon, because you project the Zenith using the longitude circles that run between the ecliptic poles. The fact that this point is always above the horizon is because the Zenith revolves around the ecliptic pole (or the other way around) in a smooth, uninterrupted fashion and the Ascendant makes 180° jumps twice a day at arctic and antarctic latitudes. That is the reason that I think the Nonagesimal is a point that is always above the horizon and that it will be 90° after the Ascendant point (and not before it) when the Ascendant is retrograde.
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Paul
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Posted: Thu Sep 06, 2018 4:03 pm    Post subject: Reply with quote

Ruud66 wrote:

About your post: I think I'm beginning to understand your approach more and more. A discussion on a forum is actually quite a difficult form of discussing things. Many of these misunderstandings would surface in minutes if you would discuss them life and in person.


True, but we'll do the best we can, it would be good to meet up one day and have a chat about this stuff.

Quote:

I understand your image and your arguments, but you confuse two concepts here: on the one hand the house system and on the other hand the projection of the sky onto the ecliptic.


Actually this isn't really the crux of my point - it's not much difference to the point I'm making if we imagine that we project the house perpendicularly from the ecliptic or project everything else perpendicularly onto the ecliptic. In practice the end result is the same. I focus I wanted to draw here is that the houses are not the "space" between two mundane arcs - what makes a house system a house system, to refer back to my older posts, is that the ecliptic is involved. Not just abstractly invovled, but crucially involved - it is the very presence and projection onto (or from) the ecliptic that makes it a house system. Keep in mind my context for why I am discussing this - it is not relevant whether we imagine all points projected perpendicularly onto the ecliptic, or indeed house lines projected perpendicularly from the ecliptic (I said the former only to make my diagram more clear.

My context is to disagree with the strength in which you made the following statements:

Sat Mar 17, 2018 2:04 pm
Quote:

The ecliptic (of course also a circle) comes in after the system was finished
...
The Placidus system is 100% mundane in nature and the ecliptic does not play a structural role. The ecliptic is just another set of points on the celestial (mundane) sphere that can be examined using the measuring rod of ascension (and descension.)


Sat Sep 01, 2018 11:01 am
Quote:

The 'actual' house system is in the mundane arcs.
...
the positions of planets and points in the houses are not dependend on their relative position to the ecliptic cusps, but they are defined on the mundane arcs.


Perhaps my posts about the ecliptic make more sense when you keep these statements of yours in mind. What I'm trying to do is point out that really we shouldn't imagine the houses as being the mundane arcs with the ecliptic either irrelevant or arbitrary to that - the houses need the ecliptic and where they intersect in order to be a house system. So when you say "the ecliptic comes after the system was finished" this seems wrong to me - the ecliptic is what finishes the system, to take phrasing. You say the ecliptic does not play a structural role, but for me what separates talking about "mundane placidus arcs" and "the placidus house system" is that the ecliptic plays no structural role in the former, but does in the latter - the structure being that we need the arcs to intersect the ecliptic to make the house. I could go as far as to say the mundane arcs are completely irrelevant everywhere EXCEPT where they hit the ecliptic. The real point I wanted to open up though is where you say "the 'actual' house system is in the mundane arcs" - because I don't know what you mean by 'actual' here, hence why I wanted to really push back and make sure we're not imagining that the mundane arcs are where the houses are - i.e. the space between two mundane arcs does not a house make. What I am trying to show is that, quite contrary to where you say "the positions of planets and points in the houses are not dependend on their relative position to the ecliptic cusps" - they are in fact PRIMARILY situated relative to the ecliptic, first and foremost, and, therefore when you say "they are defined on the mundane arcs" I cannot agree - they are not defined *on* the mundane arcs, nor even *between* the mundane arcs. They are specifically measured "on" the ecliptic, only between where those arcs hit the ecliptic. Hopefully the reason for my diagram makes more sense now.

I think some of your other posts, in this thread and the other related thread, sometimes tend to downplay the role of the ecliptic. In an early post on this thread, and in your subsequent reply to my previous post, you highlight the problem of finding house rulers. I was going to circle around this point but I'm glad you raised it explicitly. Because what I was hoping to do in my previous replies, and to nail home in this one, is that we absolutely require the ecliptic to make a house system, any house system, palcidus included, because houses are not mundane arcs (as per my diagram). But I sort of need you to acknowledge this before we can move to other issues. Those other issues being that now we, for example, accept the eclitpic's role in defining the house system itself (all houses), we can explore any problems with particular house systems - for example Placidus intersecting the ecliptic or not.

Quote:
It has become my understanding that the house system is not based on the ecliptic, because of what can happen in the horoscope beyond the polar circles, where in the Placidus system, houses can run direct and retrograde through the zodiac and the relative house position can change direction mid-house.


But this is not unique for Placidus, which is what kicked off our discussion originally. I made the point that people who rely on software and believe that the nature or definition of the MC is not important (and my experience has been that this recently occurs repeatedly with whole sign house users) fall into the trap of 'visualising' planets moving in some kind of horrific retrograde primary motion. For them, because of they think these issues are just for the silly Placidus and quadrant people to sort out, they'll be looking at a chart and not realise that if they project that chart forward a few minutes they'd see planets rising at the descendant and set at the ascendant - because of how they (or rather, their software) chooses to render the chart and determine the MC.

Now Placidus has problems, but actually all the houses run into this problem. Mars rising toward the south in the east and coming over the ascendant, will dip back under the horizon - at this point in time another planet my rise in the east, but now it's toward the north rather than the south.

This phenomenon causes problems, in terms of astrological 'orthopraxy', precisely because we do not recognise this problem widely enough. The best we can say is that quadrant house users are at least PARTIALLY aware of it. Equal and, particularly more recently, Whole sign users appear to be utterly ignorant of it and think the problem is caused solely by dividing between the ascendant and MC. And it isn't. They're incorrect. Their own house systems suffer equally - they just don't suffer by way of calcluation alone.

Quote:
If you interpet the house system for this situation as having only meaning on the ecliptic, then it is unintelligible what is happening here. There is no visible reason why the house system behaves in such a crazy way, if you just observe it in the ecliptic.


I don't disagree with any of this. In fact I'm very sympathetic to it. Really my focus here isn't on redefining how we calculate houses though - even if I suspect yours may well be to do this. I'm quite sympathetic to having mundane houses for example - it's something I've wondered about trying to program for my own experiments. Incidentally do you know of software which does this?

However, all I was ever trying to highlight is that, for right or wrong, good or bad, whether we like it or not, this is precisely how astrological software, and therefore astrologers, tend to use house systems in practice - everything is connected to the ecliptic. You make the point about latitude from the ecliptic, and I completely agree with you on this as well - we don't need to go to the poles to recognise the problems begin when we force all things onto the ecliptic (or project cusp arcs off the ecliptic - whatever way is easier to imagine it).

Quote:
To me this means that a mundane system like Placidus houses is not the right choice for finding your house rulers, not in the arctic (obviously,) and also not on the rest of the earth!


(emphasis mine) - I never really thought of that in terms of the rest of the earth. I'll have to think about this more.

Quote:

Paul wrote:
Yes, but you will also get the IC. Which one is which?

Actually, no, you will not get the IC.
What you refer to is the definition of the MC/IC as the intersection of the meridian circle with the ecliptic.


I'm going to have to push back on this - I wrote a longer reply where I explain myself, but reading further on in your post I see that actually we believe the same thing. I likewise do what you do in practice. My point was more that we have to choose to either say the MC is the culmination point or else say that it is a 'turning' point which has positive latitude. The latter is what people commonly imagine the MC to be - it doesn't take much to find someone say the Mc is the 'highest' point of the sky (despite the fact that that's the nonagesimal).

I didn't understand what you meant originally by "project the zenith across the meridian". For me, the MC is a point, but it's only a point because of astrological convention (the convention being to project everthing onto the ecliptic). I thought at first you were redefining the meridian itself, and in that world the meridian will be the 'arc' where all things culminate, and my point was that it's also where they anticulminate. But I see you mean, perhaps, if I can reword your definition, that it's not just the projection of the zenith "across" the meridian, but rather it's a projection of zenith "along" the meridian, and only between the two celestial poles.

If that's what you mean, then that's exactly what I myself believe also - this is in fact my own personal working definition of the MC though I have never seen anyone else phrase it like that. In fact my own solution, even though I'm hoping to keep myself out of this so we can focus on the 'problems' is exactly this - the MC is not necessarily above the horizon and so all astrologers need to be aware of this.

However I can also see how, based on the history of the astrological MC (by which I mean the tradition, continuing to this day, of how the MC point is used by astrologers) implies that it, as a point, is the place where a given planet gains maximum visibility. This is a problem at the poles. It is not an abstraction based on the zenith being visible, the idea was that, Jupiter, say, at the MC, is the most elevated or visible that Jupiter will ever be that day. That's a very understandable way of thinking about it - how the ancients calculated that visibility and how we do today is more or less beside the point.

If we take that definition though, then we ought to not worry too much about hte astronomical calculations, and worry more about determining the turning point of the planet such that it peaks in altitude - whether that's your (and mine) MC or not is not relevant.

This is the problem (for me). It's a problem of praxis/use and not of calculation.

Quote:
That is the reason that I think the Nonagesimal is a point that is always above the horizon and that it will be 90° after the Ascendant point (and not before it) when the Ascendant is retrograde.


Right, I was going to ignore this, but I hinted at it in other posts, because really the same problems can be applied here. If we imagine that the equal 10th has its astrological meaning conferred to it by way of applying 90º aspect along the zodiac (which people have suggested - google 'overcoming' in hellenistic astrology), then we have a big old problem again.
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astralwanderer



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Posted: Sat Sep 08, 2018 6:22 am    Post subject: Reply with quote

Hi there - many thanks for the thoughtful discussion on this topic. I've appreciated reading the debate about these important points.

Quote:
the houses are not the "space" between two mundane arcs - what makes a house system a house system, to refer back to my older posts, is that the ecliptic is involved. Not just abstractly involved, but crucially involved - it is the very presence and projection onto (or from) the ecliptic that makes it a house system.


My view is that this is a confusion of two distinct concepts and that Ruud66 has the more accurate view. In my view it doesn't logically follow that because mundane arcs may be used to identify the degrees of the ecliptic that we call house cusps, that the 'houses' themselves are created by extending great circles from these degrees of the ecliptic to the poles of the ecliptic. The fact that an astrological chart shows house boundaries encompassing a section of the ecliptic does not mean that the houses themselves are projections of these degrees through the poles of the ecliptic.

All astrologers are trying to reconcile a number of contradictory factors when representing the celestial sphere: showing a three dimensional sphere on a two dimensional page/screen; and the difference between the year (represented by the ecliptic) and the day (represented by mundane arcs/divisions).

The problem that astrologers have is that it is extremely difficult to represent two divergent planes - the ecliptic and the equator - in a single plane. Astrologers typically give primacy to the ecliptic because of the fundamental importance of the zodiac in their interpretative practice. (I see the issues here as key elements of the technical practice of astrologers, mostly lost today to computers.)

This means that mundane positions (placements in three dimensions created by the diurnal motion of the earth and the latitude of the observer) are reduced to their ecliptic positions when shown in the horoscope. However, it doesn't follow from this that house divisions are projections of great circles though the poles of the ecliptic from the point of intersection between the mundane arcs (or projections of those mundane arcs) and the ecliptic.

A good case study here is the example of the Regiomontanus house system, the Morinus house system, and the Meridian house system. All three have the same basis of mundane division - twelve equal divisions of the celestial equator, with the intersection of the meridian, and the east and west points of the horizon, with the celestial equator forming four equal quadrants.

However all systems yield different house cusps. This is because the same mundane divisions are projected into three dimensional space in different ways. This results in different degrees of the ecliptic being identified as the house cusps. However, only in one case, Morinus, is the projection of the ecliptic degree through the poles of the ecliptic used to create the 3-D house boundaries.

In the case of Regiomontanus, the divisions of the equator are projected through the north and south poles of the horizon to create 'house circles' or circles of position. It is the point of intersection between the house circles and the ecliptic that identify the degrees of the house cusps. However, the houses themselves remain the 3-D sectors created by the boundaries of the circles of position.

In the case of Morinus, the divisions of the equator, which will be exactly the same degrees of right ascension as those for Regiomontanus, are projected through the poles of the ecliptic, identifying the house cusps. In this case, and only in this case, will the houses be three dimensional divisions of the sphere at right angles to the ecliptic.

In the final case, Meridian, the divisions of the equator are projected through the poles of the equator, or the north celestial pole. The intersection of these great circles - hour circles - with the ecliptic identify the house cusps on the ecliptic. However, the boundaries of the houses are the 3-D spaces extending up to the poles of the celestial equator, not to the poles of the ecliptic.

If the latter were the case, the divisions of the equator would yield Morinus cusps not Meridian cusps.

The point is that when we talk about house divisions, it is actually the mundane division of the sphere that is primary, and the ecliptic degrees that these divisions identify are secondary. I think this is the point of divergence between the two points of view. Of course, astrologers, being ecliptic-centric and limited to showing the sphere on a 2-D plane, are interested in identifying these degrees, but it does not follow that the extension of these degrees into space through the poles of the ecliptic represent the three dimensional volumes of the houses described by the mundane division.

The actual three dimensional volumes of the houses will be a function of the specific plane of division (in the cases above - the celestial equator) and the poles that are used to extend this division into space. These may be the poles of the ecliptic (Morinus) but generally won't be except in the case of systems such as equal, M-House, Whole Sign and Porphyry.

Perhaps there's another way of putting this: there are two steps in creating astrological houses - 1. the division of the mundane sphere, creating 12 3-D segments, and 2. the identification of degrees of the ecliptic that represent this volumetric division on the plane of the ecliptic. Some systems, based on the division of the ecliptic itself, have just a single step (2) to create the volumetric division.

However, in my view, there is not an additional step, which is the projection of these degrees of the ecliptic through the poles of the ecliptic (except where the basis of the division is the ecliptic itself), to create a further 12 3-D segments of the sphere which become the volumetric houses. None of the algorithms for house calculation include this step, just steps 1 and 2. This is just as true for computer versions of the algorithms, as it is for calculations made 'by hand'.

The difficulties we are discussing do not arise from translating these algorithms into forms that computers understand, it is that we have conflicting demands, described above, when we want to represent the celestial sphere in a two dimensional form. The algorithms represent the best attempt to reconcile these demands.

I hope that this post adds something to this valuable debate. I look forward to hearing further views.
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Paul
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Posted: Sat Sep 08, 2018 8:29 am    Post subject: Reply with quote

astralwanderer wrote:
Hi there - many thanks for the thoughtful discussion on this topic. I've appreciated reading the debate about these important points.

In my view it doesn't logically follow that because mundane arcs may be used to identify the degrees of the ecliptic that we call house cusps, that the 'houses' themselves are created by extending great circles from these degrees of the ecliptic to the poles of the ecliptic. The fact that an astrological chart shows house boundaries encompassing a section of the ecliptic does not mean that the houses themselves are projections of these degrees through the poles of the ecliptic.


When you say “in my view” do you mean that you don’t think this is how it’s done, or you recognise it’s how it’s done but would prefer it’s done otherwise?

To make my diagram simpler to understand I’ve said that the houses are projected from the ecliptic - but you can say either that instead everything else is projected onto the ecliptic. The end result is the same - the former is easier to visualise or show on a diagram.

If you’re saying that in your opinion this isn’t what’s actually happening then what do you imagine is happening? If needed I’ll provide my formulae for Placidus house division I programmed and you should be able to see that the only part of the mundane arc used is the at the point where it hits the ecliptic. This is crucial to understand because house systems in practice are not equivalent to mundane arcs.

If you’re saying instead that they should be, well ok, but it’s realky related to the points I’m making which is a more a commentary on current convention and the problems we have which result from it - not his for Placidus but all houses

Quote:
Astrologers typically give primacy to the ecliptic because of the fundamental importance of the zodiac in their interpretative practice. (I see the issues here as key elements of the technical practice of astrologers, mostly lost today to computers.)


Can you expand? What specifically was lost? I don’t think I follow you.

Quote:
However, it doesn't follow from this that house divisions are projections of great circles though the poles of the ecliptic from the point of intersection between the mundane arcs (or projections of those mundane arcs) and the ecliptic.


But in practice it’s the exact same. That’s because in practice we project everything onto the ecliptic plane - ie concert 3D positions to 2D positions. But mathematically it’s equivalent to draw projection arcs from the ecliptic to the poles. 6 of one, half a dozen of the other. It’s equivalent - I prefer to imagine it as arcs from the ecliptic to better visualise it as a sphere with a coordinate system but it’s the same result either way. Incidentally it’s not the most important point of my post. The important point is you require the ecliptic - either that or you reinvent how computer programs should do this.

Quote:
A good case study here is the example of the Regiomontanus house system, the Morinus house system, and the Meridian house system. All three have the same basis of mundane division - twelve equal divisions of the celestial equator, with the intersection of the meridian, and the east and west points of the horizon, with the celestial equator forming four equal quadrants.


Neither Morinus nor meridian care about the horizon. Regio does cos it projects through the poles of the prime vertical - the north and south points of the horizon, not east and west.
Meridian divides the equator from the intersection of the meridian and projects through the poles of the equator.
Morinus does the same but projects through the poles of the ecliptic.
Neither involve the horizon.

See my posts here:
http://skyscript.co.uk/forums/viewtopic.php?t=9330

The rest of your posts correctly describes the three house systems so not sure why you say here they all use the “east and west points of the horizon”. I’m not sure what that means.


Quote:
However, the boundaries of the houses are the 3-D spaces extending up to the poles of the celestial equator, not to the poles of the ecliptic.


That’s the point though - they’re not. At least not how astrologers use them in practice. Even in meriduian system the projection through the poles of the equator intersect with the ecliptic. THOSE points are the division along the ecliptic which did our house system. If you want to imagine the house system in 2D you imagine all ponts projected to the ecliptic. In 3D you project from the ecliptic from these points through the poles of the ecliptic.

You might not agree with that - I’m not arguing it should be this way, I’m arguing it is this way.

Quote:

If the latter were the case, the divisions of the equator would yield Morinus cusps not Meridian cusps.


No, because the equator and ecliptic are not parallel.

Quote:

The point is that when we talk about house divisions, it is actually the mundane division of the sphere that is primary, and the ecliptic degrees that these divisions identify are secondary.


I started and stay engaged with these posts to clear up just these sorts of confusions. This is a very common belief and yet in practice it’s not how astrological software (or for that matter computations by hand) actually plot the houses in reality. In reality the ecliptic is of prime importance - see my diagram where venus is in the second mundane house by mundane etc but isn’t in the second house as shown by software or plotted by hand.

Quote:
but it does not follow that the extension of these degrees into space through the poles of the ecliptic represent the three dimensional volumes of the houses described by the mundane division.


Actually it does follow. The projection onto the ecliptic and focus only on where the mundane arc hits the ecliptic is the 2D convention of astrological software/practice. If you want to visualise that convention in 3D you project through the ecliptic poles. It’s equivalent. I don’t want to waste more time on this though because thinking about it for any period of time will render this fact pretty obvious. Maybe I’ll find something in a maths book to describe it if people still disagree.

Quote:

Perhaps there's another way of putting this: there are two steps in creating astrological houses - 1. the division of the mundane sphere, creating 12 3-D segments, and 2. the identification of degrees of the ecliptic that represent this volumetric division on the plane of the ecliptic. Some systems, based on the division of the ecliptic itself, have just a single step (2) to create the volumetric division.


Right, this is what I mean when I say to Ruud the system isn’t finished til the ecliptic is involved. Not sure what you mean by “volumetric” division though. Either we’re thinking in 2D, or if by 3D then it’s through the ecliptic poles which you seem to resist. The point I wanted to highlight with my diagram is that it’s not between mundane arcs.

Thanks for the input, sorry I have to disagree on some of these points. I thought it was a very simply and uncontroversial point - I had not imagined it would generate such disagreement.
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Posted: Sat Sep 08, 2018 8:32 am    Post subject: Reply with quote

A lot of typos on my last post - typing from my phone. Will correct them when I get to a desktop. Apologies if it’s hard to read!
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astralwanderer



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Posted: Sat Sep 08, 2018 10:34 am    Post subject: Reply with quote

Hi Paul - no problem - the typing seems pretty good to me.

The nub of the issue is this point:

Quote:
If you want to imagine the house system in 2D you imagine all points projected to the ecliptic. In 3D you project from the ecliptic from these points through the poles of the ecliptic.


This is the bit that I don't agree with. If it's true at all, it's only true if we take the ecliptic to be fundamental plane of reference, which we do when we look at a chart. However, if houses were really constructed in this way, I don't see how the issue of latitude error could be a problem, because the ecliptic position of the planet would be its 'true' house position.

The problem of latitude error arises precisely because the ecliptic degree position is shown in a 2-D house position, when the planet, lying off the ecliptic in 3-D, possibly occupies a neighbouring house. This is because the house cusp degree extended into space does not rise at ninety degrees to the ecliptic, except for those house systems where the ecliptic itself is the basis of the mundane division and the poles of the division are the ecliptic poles (e.g. Porphyry or equal etc).

I guess from my point of view, the astrological houses shown in the chart are always a reduction of the 3-D volume of the sphere to a plane, but there is never a corresponding and subsequent step, once this has been done, to then project the cuspal points through the poles of the ecliptic. I don't see this as a problem of imagination, it is a problem of representation - of visually showing something that has 3-D in a planar format. In my view, the calculations are a one-way trip!

I guess it's possible to look at an astrological chart and imagine that the house 'cusps' rise off the page, from each of the cuspal degrees, and meet at a pole marked by the centre of the wheel, but I don't know what it adds to our understanding. If what you are saying is that astrologers, when they look at a chart wheel, take the ecliptic positions that are identified by cusps and planets to be representative of their 'true' position in space, it's an uncontroversial point. However, I don't think it's necessary to create imaginary house boundaries based on these ecliptic positions when the cuspal degrees associated with the various forms of house division have already been identified.
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Paul
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Posted: Sat Sep 08, 2018 11:26 am    Post subject: Reply with quote

astralwanderer wrote:

This is the bit that I don't agree with. If it's true at all, it's only true if we take the ecliptic to be fundamental plane of reference, which we do when we look at a chart. However, if houses were really constructed in this way, I don't see how the issue of latitude error could be a problem, because the ecliptic position of the planet would be its 'true' house position.


The latitude of a planet is likewise projected onto the ecliptic. The only way this wouldn’t be a problem would be if, say, the ecliptic was somehow parallel to the horizon - of course nothing would rise or set. Because it’s at an angle you can easily imagine a thick band which is the ecliptic and you could have a planet with positive latitude at a given zodiacal/longitude degree and one with negative latitude at the same. Despite being at the same degree of longitude in reality one planet would peak over the horizon before the other. At a given point in time one would have risen and the other wouldn’t cos the ecliptic is at an angle to the horizon. At this moment in time one planet would be in the, say, 12th mundane house and the other in the 1st - so two planets at the same zodiacal degree could be in two different mundane houses. Yet when projected onto the ecliptic you would see them both in the same house. The degree they occupy may not appear to have risen yet even though one of the planets is over the horizon.

If I get time I’ll create a diagram later to explain it easier.
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astralwanderer



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Posted: Sat Sep 08, 2018 11:42 am    Post subject: Reply with quote

Hi Paul - just responding to some of your points:

Quote:
Neither Morinus nor meridian care about the horizon. Regio does cos it projects through the poles of the prime vertical - the north and south points of the horizon, not east and west.


I think you've misunderstood my point here; perhaps I didn't make it clearly. The basis for the mundane division is exactly the same for each of these house systems - 12 equal divisions of the celestial equator. The equator always runs through the east and west points of the horizon and crosses the upper meridian and the lower meridian.

The equal divisions are based on the tri-section of the arc of the equator running between the east point of the horizon and the upper meridian, the upper meridian and the west point of the horizon, the west point of the horizon and the lower meridian, and the lower meridian and the east point. In terms of each of these quarter arcs, they represent 90 degrees of right ascension or 6 hours in clock time.

In this sense, all the systems have a relationship with the horizon, because the east and west points of the horizon define key points in the quadrants. It's true that Meridian and Morinus don't use the ascendant (the intersection of the ecliptic and horizon in the east), but the horizon is still used to define the 12-fold division of the reference plane.

The differences in the house cusps come down to the fact the algorithms used to generate the cusps take different poles to identify the ecliptic degrees associated with each cusp.

When I say 'in my view' I'm giving my opinion about how things actually are.

On the idea of technical practice, all I am saying is that most astrologers focus on the interpretative side of practice, without much, if any regard, for the technical underpinnings of what they are looking at in a chart. I think it's a shame, but it's probably always been this way. Of course, in this age of click and generate a chart, it's even less common for an astrologer to have this level of understanding.

Quote:
The important point is you require the ecliptic - either that or you reinvent how computer programs should do this.


I'm not sure this is strictly true. It's quite possible to generate a chart wheel that refers all positions, including house cusps, to the celestial equator. It's just another way of looking at things. The use of the ecliptic is a choice or, as you say, a convention.

Quote:
Even in meriduian system the projection through the poles of the equator intersect with the ecliptic. THOSE points are the division along the ecliptic which did our house system. If you want to imagine the house system in 2D you imagine all ponts projected to the ecliptic. In 3D you project from the ecliptic from these points through the poles of the ecliptic.


It's the last sentence here that I find misses the point for me. The house cusps displayed in the chart, represented by the ecliptic degrees, are the reduction of the 3-D to the 2-D as you say in the early part of this quote. There just doesn't seem to be any need to re-imagine the sphere again, using the ecliptic projections of the cuspal points, which you describe in the final sentence. It just seems redundant to me, especially when we are looking at a chart which models the sphere as if everything exists on the ecliptic plane.

Quote:
You might not agree with that - I’m not arguing it should be this way, I’m arguing it is this way.


I'm not sure what the 'it is' in this sentence.

With reference to your diagram:

Quote:
the second mundane house by mundane etc but isn’t in the second house as shown by software or plotted by hand.


The planet is in the third house in your diagram because what is represented in the chart is its ecliptic degree in relation to the ecliptic degree associated with the house cusp. I understand your diagram. It's quite clear.

What I don't really see the need for is the second set of 'house boundaries' based on projection of the ecliptic degrees of the cusps through the poles of the ecliptic. The issue is that the great circle (generally house circles are great circles) that is generated by the division of the mundane reference plane and the projection of these divisions through the relevant pole onto the ecliptic (the curved line in your diagram), is sufficient to describe the problem. The projection of the ecliptic degree of the cusp doesn't add anything. I think that's what I really don't get - this last step just seems completely redundant.

By the way, I might have missed it, but it would be helpful to have your definition of 'mundane arc'. I think we might mean different things by this term.

Anyway, thanks for all your input on the forum Paul. I always appreciate your thoughtful posts.

Ed
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Last edited by astralwanderer on Sat Sep 08, 2018 12:04 pm; edited 1 time in total
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astralwanderer



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Posted: Sat Sep 08, 2018 11:44 am    Post subject: Reply with quote

Hi Paul - thanks for the further point - I understand what you are saying so please don't do a diagram unless you think it adds interest generally for other readers! I know that sort of artwork can take a lot of time.

Ed
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Paul
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Posted: Sat Sep 08, 2018 9:03 pm    Post subject: Reply with quote

astralwanderer wrote:

I think you've misunderstood my point here; perhaps I didn't make it clearly. The basis for the mundane division is exactly the same for each of these house systems - 12 equal divisions of the celestial equator. The equator always runs through the east and west points of the horizon and crosses the upper meridian and the lower meridian.

The equal divisions are based on the tri-section of the arc of the equator running between the east point of the horizon and the upper meridian, the upper meridian and the west point of the horizon, the west point of the horizon and the lower meridian, and the lower meridian and the east point. In terms of each of these quarter arcs, they represent 90 degrees of right ascension or 6 hours in clock time.


I mean, not really. They are all an equal division of the equator into twelve 30 degree sections starting from the meridian. Of course because the meridian is the north-south divide, 90 degrees from it will be the east and west points, which are obviously composed of three sets of 30 degrees, but we're still dividing up along the equator. The horizon doesn't come into it.

The fact that the equator can be imaged to come over the horizon to the east and west is sort of immaterial. The houses don't relate to the horizon at all (except Regio of course). Just because the equator intersects with the horizon (amongst many other great circles) is immaterial. It also intersects with the ecliptic, with the galactic centre with the prime vertical and so on. What's so special about the horizon? It doesn't get involved for the calculation for the house arcs whatsoever. I think it's a red herring to imagine that because we can say that the equator demarcates east and west that somehow meridian and morinus "have a key relationship with the horizon" - what's the key? There's nothing special or important about the horizon for these house systems. Obviously Regio is different.

So when you say...

Quote:
the horizon is still used to define the 12-fold division of the reference plane.


it really isn't. Both Morinus and Meridian can be utterly agnostic about the horizon in that sense. In fact if you think about this, take Meridian cos it's easiest to imagine. A given horizon will be unique and individual for an observer at a given latitude along the same meridian line. But the meridian houses will basically be the same, because the latitude, and by proxy the horizon, doesn't factor whatsoever in the calculation of the houses.

Quote:

The differences in the house cusps come down to the fact the algorithms used to generate the cusps take different poles to identify the ecliptic degrees associated with each cusp.


It may be worthwhile reading through this "english language" summary of the major houses I wrote a couple ofyears ago:
http://skyscript.co.uk/forums/viewtopic.php?t=9330

It's not that they take different poles to identify the ecliptic degrees per se, but rather they all take the same division and then project through different poles to create a kind of grid or coordinate system. So imagine that we have the equator, divided into twelve, and then we draw sweeping arcs up to a given pole - that is what each of the three house systems do, and they all choose a different pole. Notice that the ecliptic degrees don't come into it yet. Once we have those sweeping arcs (what we're calling mundane arcs), then we see where they intersect with the ecliptic and we flatten the entire sky into a 2D picture and these intersections along the ecliptic become our houses.

I'm not sure if this is what you're meaning or saying in your post here, but it's not that they are projected through different poles to find the ecliptic degree, they're projected as a way of dividing up the sky according to some principle. And then we find out where those arcs hit the ecliptic to determine what houses are. We might be saying the same thing, but I just want to be extra clear.

Quote:

On the idea of technical practice, all I am saying is that most astrologers focus on the interpretative side of practice, without much, if any regard, for the technical underpinnings of what they are looking at in a chart.


Well here we completely agree.

Quote:

I think it's a shame, but it's probably always been this way. Of course, in this age of click and generate a chart, it's even less common for an astrologer to have this level of understanding.


Well perhaps, but actually I don't think this was ever common knowledge when people did charts by hand either, at least not in the last century or so. Conversely, we now have a lot of software that generate charts and maps of the sky at a click and we can use those to visualise what's happening without needing to draw anything by hand or visiting those places ourselves. We might lose something, yes, but I think we gain a lot as well.

Quote:

Quote:
The important point is you require the ecliptic - either that or you reinvent how computer programs should do this.


I'm not sure this is strictly true. It's quite possible to generate a chart wheel that refers all positions, including house cusps, to the celestial equator. It's just another way of looking at things. The use of the ecliptic is a choice or, as you say, a convention.
...
When I say 'in my view' I'm giving my opinion about how things actually are.


Right, as I have said multiple times on this thread, you can do things differently, I not talking about those. I am talking about how they are actually done - whether it's convention or otherwise. If you are likewise giving your opinion about how things are actually done, then it's not important whether things could be done otherwise - they aren't. They aren't done that way.

So, to restate my point - in order to calculate houses, as we currently tend to, we need the ecliptic.

Quote:

Quote:
If you want to imagine the house system in 2D you imagine all ponts projected to the ecliptic. In 3D you project from the ecliptic from these points through the poles of the ecliptic.


It's the last sentence here that I find misses the point for me. The house cusps displayed in the chart, represented by the ecliptic degrees, are the reduction of the 3-D to the 2-D as you say in the early part of this quote. There just doesn't seem to be any need to re-imagine the sphere again, using the ecliptic projections of the cuspal points, which you describe in the final sentence. It just seems redundant to me, especially when we are looking at a chart which models the sphere as if everything exists on the ecliptic plane.


It's not that it's redundant - I am not saying project all points to the ecliptic and then also project the houses out from the ecliptic. I'm saying you can do one or the other - project everything onto the ecliptic, giving you a 2D view, or project house cusps from the ecliptic to render that 2D view in 3D.

I'm not saying do it a second time. I'm offering two ways of visualing the houses - one, we already know about, is in 2d. All charts we use typically define the houses 2-dimensionally. My diagram offers a different way of doing it - it allows it to be imagined on a 3D sphere where points/planets are not projected onto the ecliptic, but instead house cusps are projected out from it. But the end result is the exact same. I feel this should be obvious as to not require any further help from my part, but if it's not I will create a diagram, or find a maths text or something that explains it. I already feel I've wasted too much time on this as it threatens to distract from the points I'm actually making.

Quote:

I'm not sure what the 'it is' in this sentence.


As in, this is how it actually done in reality, in practice, by convention, etc. If you open up astrological software, whether we agree with this or not, that is actually what is going on under the hood. As opposed to how we might prefer to do it, or any viewpoints we have on improving how to do it.6
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astralwanderer



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Posted: Sun Sep 09, 2018 8:16 am    Post subject: Reply with quote

Hi Paul - thanks for the response. I actually think we agree on most points. The thing I just don't see the relevance of is this:

Quote:
I'm saying you can do one or the other - project everything onto the ecliptic, giving you a 2D view, or project house cusps from the ecliptic to render that 2D view in 3D.


I guess the whole point of the calculations is to render something that is in 3-D, the sphere, into 2-D, the chart, so that it can be represented in a format that's easily worked with (amongst other things).

I've just never come across someone suggesting that it's then helpful/instructive to imagine the chart in a 3-D form in the way that you have described. It just doesn't seem to add anything. From my point of view, the essential thing is to understand the compromises that are made to render the sphere into a plane in the first place, which includes accepting the difficulty of latitude error.

I understand the points you are making. The thing that I don't get is that they seem superfluous to the overall point which I think is about the issue of latitude error. I'm sorry if I don't seem to be grasping the point beyond this.

Anyway, that's enough on this topic! An interesting discussion nonetheless.

Ed
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